Question

2) (20pts) A pharmacy sells three types of syrups. Demand and cost data are summarized as: Syrup-3 Syrup-2 80 65 Syrup-1 110 2.0 2.4 600 Order cost (liras per order) Purchasing cost (liras per bottle) Holding cost (liras per bottle per year) Annual demand (bottles per year) 4.0 2.6 900 3.0 2.5 800 What should be the optimal order quantities for each type of syrup if there is a budget limitation of 1400 liras which can be used for inventory-on-hand at any given time. What will be the annual cost for this optimal solution.

Answer 1

Syrup 1 optimal order quantity

[2 * (Annual Usage in Units * Ordering Cost) / Holding Cost per Unit per year ]^(1/2)

=[2 * (600 * 110) / 2.4 ]^(1/2)= 234 units

Syrup 2 optimal order quantity

[2 * (Annual Usage in Units * Ordering Cost) / Holding Cost per Unit per year ]^(1/2)

=[2 * (900 * 80) / 2.6 ]^(1/2)=235 units

Syrup 3 optimal order quantity

[2 * (Annual Usage in Units * Ordering Cost) / Holding Cost per Unit per year ]^(1/2

=[2 * (800 * 65) / 2.5 ]^(1/2)=204 units

Holding cost for optimal order quantity for syrup 1= Average units * holding cost per unit

234/2 x 2.4= 281 liras

Ordering cost for syrup 1= (annual demand/ optimal order quantity) x ordering cost=( 600/234) x 110= 282.05

Total = 281+ 282. = 563 liras

Holding cost for optimal order quantity for syrup 2= 235/2 x 2.6= 306 liras

Ordering cost for syrup 2= (annual demand/ optimal order quantity) x ordering cost=( 900/235) x 80= 306

Total= 306 + 306= 612

Holding cost for optimal order quantity for syrup 3= 204/2 x 2.5= 255 liras

Ordering cost for syrup 3= (annual demand/ optimal order quantity) x ordering cost=( 800/204) x 65=255

Total= 255 + 255= 510

thus total cost= 563+612+510= 1685